Sets Test

Result

Sets Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

Let $$A = \{2,3,5,7,8,11\}$$ then which among the following is true?

A
$${7\notin A}$$

B
$$\{2,3\} \not\subset \ of \ A$$

C
$$ 2 \in A$$

D
None of the above

Solution

$$2\in A$$ means 2 is element of A which is true.
Question 2
1 / -0

Which of the following statements is true

A
$$3\subseteq \left\{ 1,3,5 \right\} $$

B
$$3\in \left\{ 1,3,5 \right\} $$

C
$$\left\{ 3 \right\} \in \left\{ 1,3,5 \right\} $$

D
$$\left\{ 3,5 \right\} \in \left\{ 1,3,5 \right\} $$

Solution

Element/ number three is denoted by $$3$$ and not $$\{3\}$$.
$$\{3\}$$ denotes a subset containing element 3. Hence
$$\{3\}\subseteq \{1,3,5\}$$
And
$$3\in \{1,3,5\}$$
Question 3
1 / -0

Let $$P = \{ x | x$$ is a multiple of $$3$$ and less than $$100 $$ ,$$x$$ $$\displaystyle \in $$ $$N \}$$
$$Q = \{ x | x$$ is a multiple of $$10$$ and less than $$100$$, $$x$$ $$\displaystyle \in$$ $$N\}$$

A
$$\displaystyle Q\subset P$$

B
$$\displaystyle P\cup Q=$$ $$\{ x | x$$ is multiple of 30$$ ;$$ $$\displaystyle x \in N$$$$\}$$

C
$$\displaystyle P\cap Q=\phi $$

D
$$\displaystyle P\cap Q= $$ $$\{ x | x$$ is a multiple of 30$$ ; $$ $$\displaystyle x\in N$$$$\}$$

Solution

P = $$\{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ..., 60, ...,90, ....,99\}$$
Q = $$\{10, 20, 30, 40, 50, 60, 70, 80, 90 \}$$
Then looking at the multiple choices we get
$$P \displaystyle \cap Q$$= $$\{30, 60, 90\}$$
$$\displaystyle \Rightarrow $$P $$\displaystyle \cap $$ Q = {x$$\displaystyle \mid $$ x is a multiple of 30 x$$\displaystyle \epsilon $$ N}
Question 4
1 / -0

If X and Y are two sets then $$\displaystyle X\cap (Y\cup X)'$$ equals:

A
$$X$$

B
$$Y$$

C
$$\displaystyle \phi $$

D
$$\{ 0 \}$$

Solution

We have $$\displaystyle X\cap \left ( Y\cup X \right )'=X\cap \left ( Y'\cap X' \right )$$
= $$\displaystyle X\cap Y'\cap X'=X\cap X'\cap Y'$$
= $$\displaystyle \phi \cap Y'= \phi $$
Question 5
1 / -0

If $$n (A) = 115, n(B) = 326, n(A - B) = 47$$, then $$\displaystyle n(A+B)$$ is equal to

A
373

B
165

C
370

D
None

Solution

$$n(A-B)=47\Rightarrow n(A)-n(A\cap B) = 47\Rightarrow n(A\cap B)=115-47=68$$

Hence $$n(A+B)=115+326-68=373$$
Question 6
1 / -0

Which of the following statements is true ?

A
$$\displaystyle 3\quad \subseteq \quad \left\{ 1,3,5 \right\} $$

B
$$\displaystyle 3\quad \in \quad \left\{ 1,3,5 \right\} $$

C
$$\displaystyle \{ 3\} \quad \in \quad \left\{ 1,3,5 \right\} $$

D
$$\displaystyle \{ 3,5\} \quad \in \quad \left\{ 1,3,5 \right\} $$

Solution

$$\displaystyle 3\quad \subseteq \quad \left\{ 1,3,5 \right\} $$

An element cannot be a subset of another set. Hence,false.

$$\displaystyle 3\quad \in \quad \left\{ 1,3,5 \right\} $$

$$3$$ lies in the set. Hence, true.

$$\displaystyle \{ 3\} \quad \in \quad \left\{ 1,3,5 \right\} $$

$$\{ 3\}$$ doesnot lie in the set. Hence, false.

$$\displaystyle \{ 3,5\} \quad \in \quad \left\{ 1,3,5 \right\} $$

$$\{ 3,5\}$$ doesnot lie in the set. Hence, false.

Hence, option B.
Question 7
1 / -0

Given $$\displaystyle \xi $$ = {x : x is a natural number}
A = {x : x is an even number x $$\displaystyle \in $$ N}
B = {x : x is an odd number, x $$\displaystyle \in $$ N}
Then $$\displaystyle (B\cap A)-(x-A)=....$$

A
$$\displaystyle \phi $$

B
$$A$$

C
$$B$$

D
$$A-B$$

Solution

$$A = \{2, 4, 6, 8, ........\}$$
$$B = \{1, 3, 5, 7, .......\}$$
$$\displaystyle B\cap A=\left \{ 2,4,6,8,..... \right \}\cap \left \{ 1,3,5,7,.... \right \}=\phi $$
$$\displaystyle \xi -A=\left \{ 1,2,3,4,5,6,.... \right \}-\left \{ 2,4,6,8,.... \right \}=\left \{ 1,3,5,7,.... \right \}$$
$$\displaystyle \therefore B\cap A-(\xi -A)=\phi -\left \{ 1,3,5,7,.... \right \}=\phi $$
Question 8
1 / -0

If n (A) = 120, N(B) = 250 and n (A - B) = 52, then find $$\displaystyle n(A\cup B)$$

A
$$302$$

B
$$250$$

C
$$368$$

D
None of the above

Solution

$$\displaystyle n(A-B)=n(A)-n(A\cap B)$$
$$\displaystyle \Rightarrow 52=120-n(A\cap B)$$
$$\displaystyle \Rightarrow n(A\cap B)=120-52=68$$
Now $$\displaystyle n(A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$\displaystyle =120+250-68$$
$$=302$$
Question 9
1 / -0

If A and B are two disjoint sets and N is the universal set then $$\displaystyle A^{c}\cup \left [ \left ( A\cup B \right )\cap B^{c} \right ]$$ is

A
$$\displaystyle \phi $$

B
A

C
B

D
N

Solution

Since $$A$$ and $$B$$ are disjoint sets $$B^c\cap(A\cup B)$$ will be only $$A$$ as there is no intersection between $$A$$ and $$B$$.

Of course $$A^c\cup A=N$$
Question 10
1 / -0

Suppose $$\displaystyle A_{1},A_{2}.....A_{30}$$ are thirty sets having 5 elements and $$\displaystyle B_{1},B_{2}....B_{n}$$ are n sets each with 3 elements. Let $$\displaystyle \bigcup_{i=1}^{30}Ai=\bigcup_{i=1}^{n}Bj=S$$ and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to

A
35

B
45

C
55

D
65

Solution

Since each element of S belongs to $$10$$ $$ A_{i}s$$, there are only $$15 $$elements in S $$\left[\dfrac{30\times 5}{10}\right]$$

Since each of the $$15$$ elements belongs to 9 $$B_j s$$ there are 135 elements in the second union.

No. of sets $$=\dfrac{135}{3}=45$$

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Re-Attempt Weekly Quiz Competition

Sets Test - 26

Result

Sets Test - 26

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SHARING IS CARING

Question 1

$${7\notin A}$$

$$\{2,3\} \not\subset \ of \ A$$

$$ 2 \in A$$

None of the above

Solution

Question 2

$$3\subseteq \left\{ 1,3,5 \right\} $$

$$3\in \left\{ 1,3,5 \right\} $$

$$\left\{ 3 \right\} \in \left\{ 1,3,5 \right\} $$

$$\left\{ 3,5 \right\} \in \left\{ 1,3,5 \right\} $$

Solution

Question 3

$$\displaystyle Q\subset P$$

$$\displaystyle P\cup Q=$$ $$\{ x | x$$ is multiple of 30$$ ;$$ $$\displaystyle x \in N$$$$\}$$

$$\displaystyle P\cap Q=\phi $$

$$\displaystyle P\cap Q= $$ $$\{ x | x$$ is a multiple of 30$$ ; $$ $$\displaystyle x\in N$$$$\}$$

Solution

Question 4

$$X$$

$$Y$$

$$\displaystyle \phi $$

$$\{ 0 \}$$

Solution

Question 5

373

165

370

None

Solution

Question 6

$$\displaystyle 3\quad \subseteq \quad \left\{ 1,3,5 \right\} $$

$$\displaystyle 3\quad \in \quad \left\{ 1,3,5 \right\} $$

$$\displaystyle \{ 3\} \quad \in \quad \left\{ 1,3,5 \right\} $$

$$\displaystyle \{ 3,5\} \quad \in \quad \left\{ 1,3,5 \right\} $$

Solution

Question 7

$$\displaystyle \phi $$

$$A$$

$$B$$

$$A-B$$

Solution

Question 8

$$302$$

$$250$$

$$368$$

None of the above

Solution

Question 9

$$\displaystyle \phi $$

A

B

N

Solution

Question 10

35

45

55

65

Solution

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